Fish discards are of major concern in new EU policies. Alternatives for the management of the new biomass that has to be landed is compulsory. The production of bioactive compounds from fish protein hydrolysates (FPH) has been explored in recent years. However, the viability of discards, which might account for up to 90-100% of captures in mixed trawler, gillnet, and longline industrial fisheries, to produce FPH from the muscle with bioactivities has still not been studied in terms of the optimization of the experimental conditions to enhance its production. The effect of and temperature on the hydrolysis of the muscle was mediated by three commercial proteases using response surface methodology. Temperatures of 64.6 °C and 60.8 °C and pHs of 9.40 and 8.90 were established as the best hydrolysis conditions for Alcalase and Esperase, respectively. Optimization of the best conditions for the maximization of antihypertensive and antioxidant activities was performed. Higher Angiotensin-converting enzyme (ACE) activity was found with Esperase. The optimum and temperature optimum for antioxidants were 55 °C/pH8.0 for ABTS/DPPH-Esperase, 63.1 °C/pH9.0 for DPPH-Alcalase, and 55 °C/pH9.0 for ABTS-Alcalase. No hydrolysis was detected when using Protamex.